60 kg of certain variety of rice at 32 per kg is mixed with 48 kg of another variety of rice and the mixture is sold at he average price of 28 per kg.If there be no profit or loss due to the new sale price, then the price of the second variety of rice is

Options

A. ` 25.60 per kg`
B. `25 per kg`
C. ` 23 per kg`
D. ` 30 per kg`

Answer

To solve the problem, we will follow these steps:

### Step 1: Calculate the total cost of the first variety of rice.
The first variety of rice costs 32 per kg and weighs 60 kg.

\[ \text{Total cost of first variety} = \text{Price per kg} \times \text{Weight} = 32 \times 60 = 1920 \]

### Step 2: Calculate the total weight of the mixture.
The total weight of the mixture is the sum of the weights of both varieties of rice.

\[ \text{Total weight} = 60 \text{ kg} + 48 \text{ kg} = 108 \text{ kg} \]

### Step 3: Calculate the total revenue from selling the mixture.
The mixture is sold at an average price of 28 per kg.

\[ \text{Total revenue} = \text{Average price per kg} \times \text{Total weight} = 28 \times 108 = 3024 \]

### Step 4: Calculate the total cost of the second variety of rice.
Let the price of the second variety of rice be \( x \) per kg. The total cost of the second variety is given by:

\[ \text{Total cost of second variety} = x \times 48 \]

### Step 5: Set up the equation for no profit or loss.
For there to be no profit or loss, the total cost of the mixture must equal the total revenue.

\[ \text{Total cost of first variety} + \text{Total cost of second variety} = \text{Total revenue} \]

Substituting the values we have:

\[ 1920 + 48x = 3024 \]

### Step 6: Solve for \( x \).
Rearranging the equation to find \( x \):

\[ 48x = 3024 - 1920 \]
\[ 48x = 1104 \]
\[ x = \frac{1104}{48} = 23 \]

### Conclusion:
The price of the second variety of rice is **23 per kg**.

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